Algebra Examples

$2$ , $6$ , $18$

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by $3$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 3$

Step 2

This is the form of a geometric sequence.

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of $a_{1} = 2$ and $r = 3$ .

$a_{n} = 2 \cdot 3^{n - 1}$

Step 4

Substitute in the value of $n$ to find the $n$ th term.

$a_{4} = 2 \cdot 3^{(4) - 1}$

Step 5

Subtract $1$ from $4$ .

$a_{4} = 2 \cdot 3^{3}$

Step 6

Raise $3$ to the power of $3$ .

$a_{4} = 2 \cdot 27$

Step 7

Multiply $2$ by $27$ .

$a_{4} = 54$